The manager of a chain of fast-food restaurants believes that the proportion of customers who are served within 2 minutes of placing their order is greater during lunch hours than during dinner hours. To investigate, he selects a random sample of 35 customers who placed an order during lunch hours and a random sample of 75 customers who placed an order during dinner hours. The manager finds that 71.4% of the customers were served within 2 minutes during the lunch hours and 66.7% of the customers were served within 2 minutes during the dinner hours. (a) Construct and interpret a 99% confidence interval for the difference in the proportion of the population of all dinner customers and all lunch customers who are served within 2 minutes.

(b) Does the confidence interval constructed in part (a) give the manager reason to believe that the proportion of customers who are served within 2 minutes of placing their order is greater during lunch hours than during dinner hours?

A. The 99% confidence interval for the difference in the proportion of all dinner customers and all lunch customers who are served within 2 minutes is between -0.195 and 0.289. (0.714 - 0.667) ± 2.576*(√0.714(1- 0.714)/35 + 0.667(1- 0.667)/75).

B. Since the confidence interval contains 0, we cannot conclude that the proportion of customers served within 2 minutes of placing their order is greater during lunch hours than during dinner hours.

Step-by-step explanation:

got this off chegg.

may i see the picture? it would a lot, xox

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.